match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. enter the appropriate letter (a,b,c,d, or e) in each blank.

If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

What is the condition to be congruent?

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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Answer:

n = 4

Step-by-step explanation:

Let's put all of our variables on one side, and all of our non-variable numbers on the other. (I like to do this so that the variable isn't negative. You'll still get the same answer.)

So we can minus 2n on both sides, giving us 7 = n + 3.

Then, let's do our non-variables and subtract 3 from each side. This gives us 4 = n or n = 4.

Therefore, n = 4.

When calculating simple interest, if we want to invest for months or weeks instead of years we must convert the interest rate units into years.

Option D is the correct answer

It is the interest calculated on the principal at a given rate for a time period.

We have,

The formula for simple interest.

SI = PRT/100

P = principa

R = rate

T = time

Now,

Time is in years when we are calculating the simple interest.

Example:

If time is in months.

T = 4 months

T = 4/12 = 1/3 years.

Thus,

We must convert the units into years.

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The sampling method used in this case is random sampling and the sample is representative.

A sample is a small proportion of individuals taken from the general population to be studied. For a sample to be representative it is expected that all the individuals represent the population, for example, if the population includes people of different ages the sample should include this too.

The random sample selected is representative because the seats of the students selected are distributed within the class rather than in only one row or line.

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The dimensions of the poster are given as (x^2 - 6) inches by (x^2 + 12) inches.

The area of the poster is given by the product of these two dimensions:

Area = (x^2 - 6) inches * (x^2 + 12) inches

Area = x^4 - 6x^2 + 12x^2 - 72

Area = x^4 + 6x^2 - 72 inches^2

So, the area of the poster is x^4 + 6x^2 - 72 inches^2.

The property of an isosceles trapezoid is that the diagonals are congruent. That is option C.

An isosceles trapezoid is defined as the type of quadrilateral whereby line of symmetry bisects one pair of opposite sides.

The unique characteristics of an isosceles trapezoid include the following:

Therefore, the property of an isosceles trapezoid that is listed above is that Diagonals are congruent which means that they are equal.

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The properties of isosceles trapezoid are

Two pairs of parallel sides

Two pairs of parallel sides

An isosceles trapezoid has left and right sides that are equal in length or identical in length, therefore the base angles are also equal.

The diagonals are identical because the lengths of the left and right sides are equal and the base angles are equal.

Additional varieties of trapezoids include

Generally, all trapezoids have two parallel sides.

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Lines AB, BC, and AC have an equal slope, with a slope value of 2/3.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a line AC that has an x-intercept of "2"

Since,

AB is part of line AC thus the slope of AB will be the same as the slope of line AC and the Slope of line BC.

For the slope of line AB:

Since there is no Additional data given on the problem we will assume that every square is a unit square in the graph

Thus, Coordinates of A = (-5, -2)

Since Point B is the x-intercept of line AB thus its coordinates = (-2, 0)

from the formula of the slope of a line:

m = (y₂ -y₁)/(x₂ - x₁)

Thus, the slope of line AB:

m = (0+2)/-2 +5)

m = 2/3

therefore, the slope of the line AB, BC, and AC are equal and the value of the slope is 2/3.

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Answer:

1224 cm²

Step-by-step explanation:

The picture is a rectangle with length 60 cm and width 30 cm.

area of rectangle = length × width

area of picture = 60 cm × 30 cm = 1800 cm²

Now we add the mat to the picture. The width of the mat is 6 cm, so when you add mat to two opposite sides, the total length of the picture and mat becomes 60 cm + 6 cm + 6 cm = 72 cm. When you add mat to the other two opposite sides, the total width of the picture and mat becomes 30 cm + 6 cm + 6 cm = 42 cm. Now we have a rectangle 72 cm by 42 cm.

area of picture and mat = 72 cm × 42 cm = 3024 cm²

The area of the mat is the difference in area between the picture with mat and the picture without mat.

area of mat = 3024 cm² - 1800 cm² = 1224 cm²

The least positive integer is m=132.

m(m−1)+11=N

It is clear that N must be odd and that can be divisible by the prime 11.

However, the following congruences have no solution as it is easy to prove directly by checking the few possibilities with m(m−1) not divisible by 3,5 and 7 respectively

{m(m-1)+2=0(mod 3)

{m(m-1)+1=0(mod 5)

{m(m-1)+4=0(mod 7)

Thus N=∏ with pi≥11

A necessary condition is that (solving the quadratic in m)

√4N-43=x² and from this, we need that

N≡1,3,7(mod10)

By chance, we find the minimum N=113⋅13 which corresponds to m=132

and that could have been calculated by direct trials but the next solution seems to be far from 132.

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Answer:

14

Step-by-step explanation:

When solving something like this use Pemdas

hope this help in some way

Answer:

The length of the longer ladder is 36ft

Step-by-step explanation:

30ft/10ft = 3

12ft x 3 = 36ft

Another way to solve this is by cross multiplying

[tex]\frac{10}{12}[/tex] = [tex]\frac{30}{x}[/tex]

10x = 360

x = 36ft

The solution for the equation 3x²-4x-2=0 is 1.72076 and 0.387426.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

3x²-4x-2=0

Now, solving the above Quadratic Equation

D= √b² - 4ac

From the given equation

a= 3, b-4, c=-2

Then, D= √(-4)² - 4(3)(-2)

D= √16 +24

D = √40

Now, x= (-b ±D)/ 2a

x= -(-4) ± √40/ (6)

x= 4+ √40/6  or x= 4-√40/6

x = 1.72076 or x=−0.387426

Hence, the value of x is 1.72076 and 0.387426.

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The garden can split into 20 plots.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A community garden has an area of 10 square yards.

The community wants to divide it into plots that each have an area of 1/2 square yard.

The number of community garden,

= 10/(1/2)

= 20

Therefore, the number of required plots is 20.

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The value of the integral is given as follows:

C. -7π/2.

The result of the integral is given by the total area of the figure.

From x = -7 to x = -1, the figure is a semi-circle of radius 3, below the y-axis, hence it's area is given as follows:

A1 = -0.5π x 3²

A1 = -4.5π.

From x = -1 to x = 1, with the line, the figure is a right triangle with sides 2 and 2, hence the area is given as follows:

A2 = 0.5 x 2 x 2

A2 = 2.

From x = 1 to x = 3, the figure is quarter circle with radius 2, hence the area is given as follows:

A3 = 0.25π x 2²

A3 = π.

From x = 3 to x = 4, the figure is a right triangle with sides 1 and 4, below the y-axis, hence the area is given as follows:

A4 = 0.5 x 1 x 4

A4 = -2.

Hence the total area, representing the integral, is given as follows:

A = A1 + A2 + A3 + A4

A = -4.5π + 2 + π - 2

A = -3.5π

A = -7π/2.

(the result of the integral is negative but the area is positive).

Meaning that the correct option is given by option C.

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Step-by-step explanation:

y÷15 or y/15 = 6

let's ignore the remainder for a moment.

y/15 = 6

y = 6×15 = 90

now, what does "remainder" mean ?

it means after a clean division there is a result, and there is still this additional remainder left.

the actual result of

a/b is

a/b = c + remainder/b

where c is an integer, and remainder is also an integer.

so, a = b×c + b×remainder/b = b×c + remainder

therefore,

y = 6×15 + 8 = 98

to check

98/15 = 6 remainder 8

so, it is correct

314÷y = 18 remainder 8

314 = 18y + 8

306 = 18y

y = 306/18 = 17

check

314 / 17 = 18 remainder 8

so, it is correct.

The size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I would be 5530

The size of bands resulting from cutting a plasmid with Hind III, EagI and SmaI can be determined using the following formula:

Size of Band = Plasmid Size - (Hind III + EagI + SmaI)

The size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I can be calculated using the following formula:

For this example, the plasmid has a size of 5541 base pairs. After cutting with Hind III, EagI and SmaI, the size of the bands will be:

Size of Band = 5541 - (6 + 4 + 4)

Size of Band = 5527 base pairs

Band size = Total base pairs - [size of sites (Hind III + Eco RI + Sma I)] + 1

In this case, the band size would be calculated as follows:

Band size = 5541 - (6 + 6 + 4) + 1

Band size = 5530 bp

Therefore, the size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I would be 5530

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Complete question:

What size bands would result from cutting the following plasmid using Hind III, EcoRI and SmaI? The plasmid has a total of 5541 base pairs.

If the sequence be 2, 9, 22, 45, 82, 137, 214 then the pattern be 6, 13, 23, 37, 55, 77.

The term "patterns" describes common, repeatable sorts of practices or regulations. To forecast what has happened or what might happen, patterns are helpful. come following a group of integers that are ordered specifically. Sequence describes this grouping of numbers.

Putting events or information in a precise order is referred to as sequencing. Higher-order thinking abilities—such as those for detecting patterns, figuring out causes and effects, and more—are necessary for sequencing. Sequencing aids students in both understanding and organizing the material they have learnt and in problem-solving.

Let the given sequence be 2, 9, 22, 45, 82, 137, 214

The differences to a pattern in the sequence be

= 9 - 2, 22 - 9, 45 - 22, 82 - 45, 137 - 82, 214 - 137

= 6, 13, 23, 37, 55, 77

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Using the subtraction operation, the number of flowers with 10 petals that Mrs. Moth picked was 6.

A subtraction operation is one of the four basic mathematical operations, including addition, division, and multiplication.

The subtraction operation involves the minuend, the subtrahend, and the difference.

The minuend is the number or value being subtracted from by the subtrahend.  The result of a subtraction operation is known as the difference.

The total number of picked flowers = 24

The number of flowers with 9 petals = 6

The number of flowers with 8 petals = 7

The number of flowers with 3 petals = 5

The total number of flowers identified = 18 (6 + 7 + 5)

The number of flowers with 10 petals = x

x = 24 - 18

= 6

Thus, 6 flowers had 10 petals out of the 24 Mrs. Moth picked.

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Answer: letra “q” no es un número

Step-by-step explanation:

According to the given information in the question the inverse of y=2x²+3x+5 is x = (y - 5 - 3x)/2.

Inverse operations, such as subtraction and addition multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The opposite of a number, or "inverse," is what is meant by the phrase. i.e., x - 1 = 1 / x.

Negative correlation and inverse relationships are interchangeable terms. Any two or more variables that consistently move in the opposing directions can be described by both. The outcome of measuring an inverse association will result in a negative sign.

To find the inverse of a function, you first need to switch the x and y variables, and then solve for y.

So, the inverse of y=2x²+3x+5 is x = (y - 5 - 3x)/2

Note that the inverse of a function is only possible if the function is a one-to-one function.

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Answer:

x = 25

Step-by-step explanation:

Since the given triangle is a right triangle and we are also given two sides which are opposite (height) = 24 units and adjacent (base ) = 7 units. We can apply the Pythagoras Theorem where:

[tex]\displaystyle{\text{opposite}^2 + \text{adjacent}^2 = \text{hypotenuse}^2}[/tex]

In simpler words, it is:

[tex]\displaystyle{\text{height}^2 + \text{base}^2 = \text{slope}^2}[/tex]

Substitute in given values:

[tex]\displaystyle{24^2+7^2=x^2}[/tex]

Evaluate and solve for x:

[tex]\displaystyle{576+49=x^2}\\\\\displaystyle{625=x^2}\\\\\displaystyle{\sqrt{625}=\sqrt{x^2}}\\\\\displaystyle{\pm \sqrt{625}=x}\\\\\displaystyle{\pm 25=x}[/tex]

However, x is a length value and length's value cannot be negative so x can only be 25.

Hence, x = 25 units

The single payment that is required to settle both debts is given as follows:

$3,897.9.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which:

For the $2,100 payment in 6 months = 0.5 years, the principal is obtained as follows:

(1 + 0.5 x 0.063) P = 2100

P = 2100/(1 + 0.5 x 0.063)

P = $2,035.88.

For the $1,950 payment in 9 months = 0.75 years, the principal is obtained as follows:

(1 + 0.75 x 0.063) P = 1950

P = 1950/(1 + 0.75 x 0.063)

P = $1,862.02.

Hence the single payment is obtained as follows:

2035.88 + 1862.02 = $3,897.9.

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Following are the answers to all the asked questions for classifying types of cost.

a. Electricity costs of $0.025 per kilowatt-hour - variable cost

b. Warehouse rent of $6,000 per month plus $0.50 per square foot of storage used - mixed cost

c. Thread - variable cost

d. Lubricants used to oil machinery - variable cost

e. Janitorial costs of $2,000 per month - fixed cost

f. Advertising costs of $10,000 per month - fixed cost

g. Sales salaries - fixed cost

h. Color dyes for producing different colors of sweatshirts - variable cost

i. Salary of the production supervisor - fixed cost

j. Patterns for different designs. Patterns typically last many years before being replaced - fixed cost

k. Maintenance cost with sewing machine company. The cost is $2,000 per year plus $0.001 for each machine hour of use - mixed cost

l. Property taxes on factory, building, and equipment - fixed cost

m. Cotton and polyester cloth - variable cost

n. Hourly wages of sewing machine operators - variable cost

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By calculating, The GCF of the given numbers 49 and 28 is 7.

What is Algebraic expression ?

An algebraic expression is an expression that consists of numbers, variables and operators such as addition, subtraction, multiplication and division. These expressions can be used to solve equations and other mathematical problems. Algebraic expressions can also be used to represent relationships between different variables. For example, the expression 4x + 2y can be used to represent the relationship between two variables, x and y.

So lets first find the prime factorization of 28

prime factorization of 28 = 2 × 2 × 7

So lets first find the prime factorization of 49

prime factorization of 49 = 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, The GCF  of the  given numbers 49 and 28 is 7.

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Variable x and y for the rectangle is given by

x = (3x + 3)/6 + 1

y = (3x + 3)/6

Yes that's right. You have to equate the expressions for widths and for the lengths, since left and right widths (and lengths) have the same dimensions.

You may rewrite the equation for y=3x+3÷6 as

y = (3x + 3)/6

And now you have an expression for y, we can substitute it to the other equation you got:

x = y + 1

x = (3x + 3)/6 + 1

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The possible length of the third side of a triangle, say x, with the other two sides are 5 inches and 12 inches. is  

7 ≥ x ≥ 17

The length of the third side is within the range of

The sum of the two ides is the highest possible length of the third side

= 12 inches + 5 inches

= 17 inches

The difference of the two ides is the lowest possible length of the third side

= 12 inches - 5 inches

= 7 inches

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The correct description of each function term is given as follows:

1. Input: A rule to determine the value of the output.

2. Output: The result of applying a function rule to the value of an input, and is the dependent variable.

3. Domain: the set of allowable inputs.

4. Range: The set of possible outputs.

5. Function: A relation in which each input has only one output.

A function has the notation y = f(x), in which.

Hence the input is applied to the function to obtain the output, and these concepts, along with domain and range, are presented in this problem.

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Answer:

The expression "5.25x + 1246x" is equivalent to "1771x"

Using complementary angles, the value of x = 10.3

Complementary angles are angles in which the sum add up to 90°.

Since in a right triangle, sin(8x - 9) = cos(x + 6). To solve the problem, we proceed as follows.

sin(8x - 9) = cos(x + 6).

Given that cosФ = sin(90 - Ф), we have that

cos(x + 6) = sin[90 - (x + 6)]

So, susbstituting this into the equation, we have that

sin(8x - 9) = cos(x + 6)

sin(8x - 9) = sin[90 - (x + 6)]

This implies that

8x - 9 = 90 - (x + 6)

8x - 9 = 90 - x - 6

8x - 9 = 84 - x

Adding x to both  sides of the equation, we have

8x + x - 9 = 84 - x + x

9x - 9 = 84 + 0

9x - 9 = 84

Adding 9 to both sides of the equation, we have that

9x - 9 + 9 = 84 + 9

9x + 0 = 93

9x = 93

x = 93/9

x = 10.33

x ≅ 10.3

So, the value of x = 10.3

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